Chapter 12 Exercise 12

Hi Vasco

A tiny point in your answer for the algebraic part of the question. In both cases you get to the answer by appealing to the geometric proof. This is unconvincing as an algebraic solution must stand on its own if it is to be an 'algebraic' solution. You are forced to argue that because the fluxes are the same before and after the mapping, the source strength must be the same...in which case you didn't need the algebra in the first place. You are relying on the geometric solution to buttress your algebraic solution.

Your difficulty arises because you introduce a new constant tilde S in the mapped plane and then have to try and prove why tilde S = S. This you cannot do purely with algebra because it is a an introduction not required by the situation. That is, you do not need to introduce tilde S.

A mapping rotates and amplifies coordinate dependent entities. S is just a scalar so is unaffected by a mapping. So after the mapping S will still be S. The question is whether an expression for source strength after the mapping will reduce to S or some other expression involving S.

The fact that your expressions for source strength after the mapping does reduce to S (or S/n) is the proof you seek. You do not need to appeal to i).


telemeter